Population effects on the red giant clump absolute magnitude, and distance determinations to nearby galaxies

The red giant clump has been recently argued to be a reliable distance indicator for the galaxies in the Local Group. The accuracy of distance determinations based on this method, however, depends on the possible presence of systematic magnitude differences (DeltaM(I)(RC)) between the local clump revealed by the Hipparcos colour-magnitude diagram (CMD), and the clump stars observed in distant galaxies. In this paper, we re-address the problem of these systematic 'population' effects. First, we present tables with the theoretically predicted I-band clump magnitude as a function of age and metallicity. Simple equations, taken from basic population synthesis theory, are provided for the easy computation of the mean clump magnitude for any given galaxy model. We use our models to explain in some detail what determines the distribution of masses, ages and metallicities of clump stars in a galaxy. Such an approach has so far been neglected in the analysis of clump data related with distance determinations. We point out that, in galaxies with recent/ongoing star formation (e.g. the discs of spirals), the age distribution of clump stars is strongly biased towards younger (similar to1-3 Gyr) ages, and hence towards higher metallicities. Obviously, this does not happen in galaxies with predominantly old stellar populations (e.g, ellipticals and bulges). We construct detailed models for the clump population in the local (Hipparcos) sample, the bulge, Magellanic Clouds and Carina dSph galaxy. In all cases, star formation rates and chemical enrichment histories are taken from the literature. The Hipparcos model is shown to produce distributions of metallicities, colours, and magnitudes, that are similar to those derived from spectroscopic and Hipparcos data. The bulge, Magellanic Clouds, and Carina dSph models are used to analyse the values of DeltaM(I)(RC) for these different stellar systems. We show how the clump-RR Lyrae data from Udalski are well reproduced by the models. However, despite the similarity between the models and data, the models indicate that the Linear DeltaM(I)(RC) versus [Fe/H] relations that have been derived from the same data (such as by Udalski and Popowski) are not general. In fact, the distribution of clump stars has several factors hidden in it - e.g. the age-metallicity relation, the rate of past star formation - that cannot be described by such relations. The model behaviour is also supported by empirical data for open clusters by Sarajedini and Twarog et al. We argue that Udalski's data for Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) star clusters do not allow a good assessment of the age dependence of the clump magnitude. Moreover, we remark that similar analyses of cluster data should better include clump stars with ages 1-2 Gyr, which turn out to be very important in determining the mean clump in galaxies with recent star formation. Finally, we provide revised clump distances to the bulge, Magellanic Clouds and Carina dSph, and further comment on their reliability. The largest DeltaM(I)(RC) values are found for the Magellanic Clouds and Carina dSph, which turn out to be located at distance moduli similar to0.2-0.3 mag longer than indicated by works which ignore population effects. The Galactic bulge, instead, may be slightly closer (up to 0.1 mag in distance modulus) than indicated by previous works based on the red clump, the exact result depending on the use of either scaled-solar or alpha -enhanced stellar models.